Thirty seven million people in the United States do not have health insurance. Policies to rectify this situation are devised under the assumptions of the traditional theory of expected utility maximization as a method of choice under uncertainty. This theory predicts that low income people get the most utility from insuring against an expected loss. This implies that reducing the price of health insurance to an affordable level would lead to a large increase in the purchase of health insurance by low income people. An alternative theory of expected utility maximization is presented which describes a different situation. Here, people do not gain utility from the purchase of health insurance until they have reached a level of income above that necessary to meet basic needs. In this case, a reduction in the price of health insurance for low income people might not suffice to make it a desirable purchase as long as the premium remained too high to budget for basic needs as well. Health insurance would only be desired by people at levels of income above that necessary to meet basic needs. This study will test the hypotheses of the traditional and alternative theories of expected utility maximization by modeling the demand for health insurance in the form of a model of discrete choice of health plan by employed people who have already made the choice to purchase some health insurance. It will attempt to identify patterns in the demand for health insurance with respect to income and price that have implications for the lack of demand seen at low income levels. In addition it will attempt to clarify the appropriate conceptualization of income and price within such a model.